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PreprintCC BY 4.0arXiv

The Free Scalar as a Thermal Envelope for Three-Dimensional CFTs

  • Christopher P. Herzog
  • Andreas Stergiou
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Abstract

We conjecture that every unitary three-dimensional conformal field theory obeys cS/CT≤16πζ(3), where s=cST2 is the thermal entropy density and CT the stress-tensor two-point coefficient, with equality for free scalars. We embed this in a stronger conjecture: on S1× H2, the CT-normalized hyperbolic heat capacity is bounded above by that of the free scalar for all T≥(2πR)−1. Near the conformal temperature, for theories smooth from the high-temperature side and without boundary terms in the modular Hamiltonian, the heat-capacity bound follows from conformal-collider positivity. We test the conjectures in free, interacting large-N, and holographic theories. Monte Carlo data for the three-dimensional Ising and O(N) models also obey the flat-space bound.

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Cite

BibTeXRIS
BibTeX
@misc{herzog2026free,
  title = {{The Free Scalar as a Thermal Envelope for Three-Dimensional CFTs}},
  author = {Christopher P. Herzog and Andreas Stergiou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33179},
  eprint = {2610.33179},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33179},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Free Scalar as a Thermal Envelope for Three-Dimensional CFTs
AU  - Christopher P. Herzog
AU  - Andreas Stergiou
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33179
UR  - https://arxiv.org/abs/2610.33179
AB  - We conjecture that every unitary three-dimensional conformal field theory obeys c_S/C_T≤16πζ(3), where s=c_ST^2 is the thermal entropy density and C_T the stress-tensor two-point coefficient, with equality for free scalars. We embed this in a stronger conjecture: on S^1× H^2, the C_T-normalized hyperbolic heat capacity is bounded above by that of the free scalar for all T≥(2πR)^−1. Near the conformal temperature, for theories smooth from the high-temperature side and without boundary terms in the modular Hamiltonian, the heat-capacity bound follows from conformal-collider positivity. We test the conjectures in free, interacting large-N, and holographic theories. Monte Carlo data for the three-dimensional Ising and O(N) models also obey the flat-space bound.
ER  -